Grub boots to Maintenance Shell

[fehlix]

What is the safest and best way to reinstall MX Linux?

Perhaps, also get lasted ISO from monthly snapshot.
Make sure you boot the LiveUSB/ISO in UEFI-boot mode, the same as Linux Mint was installed, and not in legacy BIOS/CSM/MBR boot mode. And probably run full upgrade within the live session first.
During install select existing ESP and install "GRUB" onto ESP.
When rebooting, you may select the UEFI boot loader (either Ubunt/Mint or MX Linux) from F12-boot options menu
( if enabled with UEFI System Setup).
Incase the MX Linux entry is not shown with the Linux Mint's GRUB menu ( after running sudo update-grub),
it may relate to the recent change where os-prober may have been disabled in Ubuntu/Mint's grub.

[poyt448]

Thanks to everyone who assisted. Shall I mark this as "Solved"? Wiping a hard drive partition and reinstalling MX Linux plus all the usual files isn't much like a solution to me. Disappointed we couldn't fix up the initial error through better remedial software processes. I'm advised that this predicament was possibly caused by software such as Grub Customizer and Boot Repair. Perhaps Linux users should be made more aware of the effects of such applications.

[asqwerth]

Thanks to everyone who assisted. Shall I mark this as "Solved"? Wiping a hard drive partition and reinstalling MX Linux plus all the usual files isn't much like a solution to me. Disappointed we couldn't fix up the initial error through better remedial software processes. I'm advised that this predicament was possibly caused by software such as Grub Customizer and Boot Repair. ...

To be frank, I believe it was caused by you initially installing MX as legacy boot when your system (via Mint being your first installed distro) was already set up as a UEFI boot machine.

As to how it can happen, you have to check your machine's BIOSs setting's boot order. The hardware's BIOS could have been set up to favour booting a USB as legacy boot before UEFI boot. Once that happens, and you boot the live USB as legacy, then MX will be installed as legacy (ie the installer will be asking you which MBR to install bootloader instead of where the EFI partition is). Which conflicts with your UEFI system.

[MXRobo]

@poyt448
Notice UEFI in lower left corner.
https://youtu.be/gy_uVyjK6go?t=24
HTH